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 A321897 Irregular triangle read by rows where T(H(u),H(v)) is the coefficient of p(v) in h(u) * Product_i u_i!, where H is Heinz number, h is homogeneous symmetric functions, and p is power sum symmetric functions. 3
 1, 1, 1, 1, 0, 1, 2, 3, 1, 0, 1, 1, 6, 3, 8, 6, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 2, 3, 1, 24, 30, 20, 15, 20, 10, 1, 0, 0, 0, 1, 1, 120, 90, 144, 40, 15, 90, 120, 45, 40, 15, 1, 0, 6, 0, 3, 8, 6, 1, 0, 0, 2, 3, 2, 4, 1, 0, 0, 0, 0, 1, 720, 840, 504, 420, 630 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Row n has length A000041(A056239(n)). The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). LINKS Table of n, a(n) for n=1..77. Wikipedia, Symmetric polynomial EXAMPLE Triangle begins: 1 1 1 1 0 1 2 3 1 0 1 1 6 3 8 6 1 0 0 1 0 1 0 2 1 0 0 2 3 1 24 30 20 15 20 10 1 0 0 0 1 1 120 90 144 40 15 90 120 45 40 15 1 0 6 0 3 8 6 1 0 0 2 3 2 4 1 0 0 0 0 1 720 840 504 420 630 504 210 280 105 210 420 105 70 21 1 0 0 0 1 0 2 1 For example, row 14 gives: 12h(41) = 6p(41) + 3p(221) + 8p(311) + 6p(2111) + p(11111). CROSSREFS Row sums are A321898. Cf. A005651, A008480, A056239, A124794, A124795, A319193, A321742-A321765, A321896. Sequence in context: A079343 A004566 A321896 * A050074 A346688 A278313 Adjacent sequences: A321894 A321895 A321896 * A321898 A321899 A321900 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Nov 20 2018 STATUS approved

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Last modified September 11 08:57 EDT 2024. Contains 375814 sequences. (Running on oeis4.)